New payload concepts of low cost earth stations for future mobile satellite communications can only be realised by using dedicated on-board processing satellites. The satellite uplink and downlink are optimised by the use of FDMA/SCPC for uplink and TDM on the down link. This scheme allows mobile transmitters to transmit a narrow band, low power signal, resulting in smaller dishes and HPAs with lower output power. On the uplink, there are hundreds of FDM channels to be demodulated on-board. The most promising approach is the use of all-digital multicarrier demodulators (MCDs), where analogue and digital hardware are efficiently shared amongst the channels and digital signal processing is used at an early stage to take advantage of VLSI technology. A MCD consists of a channeliser for separation of FDM channels followed by individual demodulators for each channel. The major research areas in MCD's are efficient implementation of channelisers and the optimal demodulation algorithms for the demodulator. This thesis is focused on the demodulator part of an MCD using OQPSK modulation which haye received attention recently due to its spectral advantages in non-linear mobile satellite channels. Most of the research carried out on the OQPSK modulation has been addressed to its spectral performance under satellite channel non-linearities, but little attention has been paid to efficient receiver designs. The most important requirements of the demodulator in a mobile environment is fast acquisition with minimum overhead. This over-head includes long preambles in data frames to aid the acquisition of the carrier and the symbol timing recovery loops. In this thesis, research on preambleless all-digital demodulators for OQPSK has been carried out. The performance of the most suitable OQPSK synchronisation algorithms have been evaluated using extensive computer simulations. These algorithms have been selected after a comprehensive survey of digital synchronisation techniques. It is shown how these algorithms are related to the maximum likelihood (ML) principle and these algorithms are classified according to their technique of parameter extraction from the likelihood function. The synchronisation problems associated with OQPSK are pointed out with possible solutions. On the basis of the performance results of individual synchronisers, various demodulation algorithms for OQPSK have been developed for fixed, mobile and deep space applications. The DSP implementation of the all- digital OQPSK demodulator developed for the MCD for mobile applications is described in detail and its performance compared with simulation results.